Help with copper pipe leak above water softener

Right above there water softener there are three valves. The valve on the right seems to be leaking. I am not sure if it is the nut, or the actual copper pipe where it goes into the female end of the valve.

I tightened the nut and it seems to have stopped.

My question is, could it be possible that when the water softener kicks on it loosened up the nut, in turn causing the leak?

If not, or maybe in addition, should I reinforce the opening at the male/female portion of the copper pipe?

Leaks in these older "gate valves" are common, and the usual (temporary) fix is to tighten the "bonnet" or "packing nut" as you have done. Sometimes the position of the valve (fully open or not) affects the leak. Longer term, you can re-pack the valve (a fairly simple operation) or replace the valve with a new ball valve. If you're going to replace the valve, you might as well do all 3, basically building a new bypass-valve assembly. But, if you've stopped the leak with a simple tightening of the packing nut, you're probably good for another 10 years.